Text of 11.3 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Perimeter and...
11.3 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Perimeter and Area of Similar Figures
11.3 Warm-Up 1. Two polygons are similar and the ratio of corresponding sides is 3 : 4. What is the ratio of the perimeters? 2. Solve. 12 x = 18 6 ANSWER 3 : 4 ANSWER 4
11.3 Warm-Up 3. A rectangle has area 108 square feet and the length is three times the width. What are the dimensions of the rectangle? ANSWER 18 ft by 6 ft
11.3 Example 1 Ratio (red to blue) of the perimeters a.a. Ratio (red to blue) of the areas b.b. In the diagram, ABC DEF. Find the indicated ratio. a. By Theorem 6.1 on page 374, the ratio of the perimeters is 2:3. b. By Theorem 11.7 above, the ratio of the areas is 2 2 :3 2, or 4:9. SOLUTION The ratio of the lengths of corresponding sides is 12 8 = 3 2, or 2:3.
11.3 Example 2 SOLUTION The ratio of a side length of the den to the corresponding side length of the bedroom is 14 : 10, or 7 : 5. So, the ratio of the areas is 7 2 : 5 2, or 49 : 25. This ratio is also the ratio of the carpeting costs. Let x be the cost for the den.
11.3 Example 2 25 49 = 225 x cost of carpet for den cost of carpet for bedroom x 441 = Solve for x. ANSWER It costs $441 to carpet the den. The correct answer is D.
11.3 Guided Practice 1. The perimeter of ABC is 16 feet, and its area is 64 square feet. The perimeter of DEF is 12 feet. Given ABC ~ DEF, find the ratio of the area of ABC to the area of DEF. Then find the area of DEF. ; 36 ft 2 9 16 ANSWER
11.3 Example 3 Then use Theorem 11.7. If the area ratio is a 2 : b 2, then the length ratio is a:b. Cooking A large rectangular baking pan is 15 inches long and 10 inches wide. A smaller pan is similar to the large pan. The area of the smaller pan is 96 square inches. Find the width of the smaller pan. SOLUTION First draw a diagram to represent the problem. Label dimensions and areas.
11.3 Example 3 Area of smaller pan Area of large pan = 150 96 = 25 16 Write ratio of known areas. Then simplify. Find square root of area ratio. = 4 5 Length in smaller pan Length in large pan Any length in the smaller pan is, or 0.8, of the corresponding length in the large pan. So, the width of the smaller pan is 0.8(10 inches ) 8 inches. 4 5 =
11.3 Example 4 The floor of a gazebo is a regular octagon. Each side of the floor is 8 feet, and the area is about 309 square feet. You build a small model gazebo in the shape of a regular octagon. The perimeter of the floor of the model gazebo is 24 inches. Find the area of the floor of the model gazebo to the nearest tenth of a square inch. Gazebo
11.3 Example 4 SOLUTION All regular octagons are similar, so the floor of the model is similar to the floor of the full-sized gazebo. STEP 1 Find the ratio of the lengths of the two floors by finding the ratio of the perimeters. Use the same units for both lengths in the ratio. Perimeter of full-sized Perimeter of model = 8(8 ft ) 24 in. = 64 ft 2 ft = 32 1 So, the ratio of corresponding lengths (full- sized to model) is 32:1.
11.3 Example 4 STEP 2 Calculate the area of the model gazebos floor. Let x be this area. (Length of full-sized) 2 (Length of model) 2 Area of full-sized Area of model = 309 ft 2 x ft 2 32 2 1212 = Theorem 11.7 Substitute. 1024x 309= Cross Products Property x 0.302 ft 2 Solve for x.
11.3 Example 4 STEP 3 Convert the area to square inches. 0.302 ft 2 144 in. 2 1 ft. 2 43. 5 in. 2 The area of the floor of the model gazebo is about 43.5 square inches.
11.3 Guided Practice 2. The ratio of the areas of two regular decagons is 20:36. What is the ratio of their corresponding side lengths in simplest radical form? ANSWER 5 3
11.3 Guided Practice 3. Rectangles I and II are similar. The perimeter of Rectangle I is 66 inches. Rectangle II is 35 feet long and 20 feet wide. Show the steps you would use to find the ratio of the areas and then find the area of Rectangle I. 66 1320 = 1 20 1 400 is the ratio of sides, so the ratio of areas is, 252 in. 2 ANSWER
11.3 Lesson Quiz Figure I Figure II. Find the ratio of the perimeters and the ratio of the areas. Then find the unknown area. ANSWER Ratio of perimeters: 4:3; ratio of areas: 16:9; 33.75 ft 2 1. A = 60 ft 2
11.3 Lesson Quiz Figure I Figure II. Find the ratio of the perimeters and the ratio of the areas. Then find the unknown area. 2. A = 780 cm 2 ANSWER Ratio of perimeters: 2:3; ratio of areas: 4:9; 346 cm 2 2 3
11.3 Lesson Quiz 3. Rectangle I Rectangle II. In Rectangle I, the length is 20 feet and the perimeter is 64 feet. In Rectangle II, the width is 8 yards. Find the ratio of the area of Rectangle I to the area of Rectangle II. ANSWER 121 : 144